Solve the Boundary-Value Problem, If Possible $$y ^ { tt } + 5 y ^ { t } - 24 y = 0 , y ( 0 ) = 0 , y ( 2 ) = 1$$

question 113

Multiple Choice

Solve the boundary-value problem, if possible.
$$y ^ { tt } + 5 y ^ { t } - 24 y = 0 , y ( 0 ) = 0 , y ( 2 ) = 1$$

• A) \(y ( x ) = \left( e ^ { 6 } - e ^ { - 16 } \right) ^ { - 1 } \left( e ^ { 3 x } - e ^ { - 8 x } \right)\)
• B) \(y ( x ) = \left( e ^ { 8 } - e ^ { - 16 } \right) ^ { - 1 } \left( e ^ { x } - e ^ { - 8 x } \right)\)
• C) \(y ( x ) = \left( e ^ { 3 } - e ^ { - 16 } \right) \left( e ^ { 3 x } - e ^ { - 8 x } \right)\)
• D) \(y ( x ) = \left( e ^ { 3 } - e ^ { - 16 } \right) ^ { - 1 } \left( e ^ { 3 x } - e ^ { - 8 x } \right)\)
• E) No solution

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Definitions:

Physical Units Method

A technique in accounting used to measure output in production or inventory in terms of the total number of units.

Joint Production Costs

Costs incurred in the process where two or more products are produced together and the costs cannot be readily assigned to individual products.

Contribution Margin

A measure of profitability calculated as sales revenue minus variable costs; used to evaluate a product's contribution to covering fixed costs.

Machine Hour

A measure of production time or operation, calculated as the total hours a machine is run in the production process.